Question 1192634: In the movie Forrest Gump, the public school required an IQ of at least 80 for admittance. IQ test scores are normally distributed with mean 100 and standard deviation 16
a. What percentage of people would qualify for admittance to the school.
b. If the public school wishes 95 percent of all children to qualify for admittance, what minimum IQ test score should be required for admittance?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **a. Percentage of people who would qualify:**
* **Calculate the z-score:**
* z = (X - μ) / σ
* where:
* X = cutoff score (80)
* μ = mean (100)
* σ = standard deviation (16)
* z = (80 - 100) / 16 = -1.25
* **Find the area under the standard normal curve:**
* Use a z-table or a calculator to find the area to the right of z = -1.25.
* This area represents the proportion of people with an IQ score of 80 or higher.
* **The area to the right of z = -1.25 is approximately 0.8944.**
* **Therefore, approximately 89.44% of people would qualify for admittance.**
**b. Minimum IQ score for 95% admittance:**
* **Find the z-score corresponding to the 95th percentile:**
* Use a z-table or a calculator to find the z-score that corresponds to an area of 0.95 to the left of it.
* This z-score is approximately 1.645.
* **Calculate the corresponding IQ score:**
* X = μ + z * σ
* X = 100 + 1.645 * 16
* X = 126.32
* **Therefore, the minimum IQ score required for admittance should be approximately 126.**
**In summary:**
* **a.** 89.44% of people would qualify for admittance with an IQ cutoff of 80.
* **b.** To ensure 95% of children qualify, the minimum IQ score should be approximately 126.
Answer by ikleyn(52810)  (Show Source):
You can put this solution on YOUR website! .
The movie Forrest Gump, the public school required an IQ of at least 80 for admittance.
IQ test scores are normally distributed with mean 100 and standard deviation 16
(a) What percentage of people would qualify for admittance to the school.
(b) If the public school wishes 95 percent of all children to qualify for admittance,
what minimum IQ test score should be required for admittance?
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The solution and the answer for part (b)
in the post by @PChill both are INCORRECT.
His error is that he interprets 95%, or 0.95, as the area on the LEFT of the row mark,
while, in reality, 95%, or 0.95, is the area on the RIGHT of the row mark.
+--------------------------------------------------+
| Indeed, they want to take 95% among the best |
| - - - not 95% among the worst ! |
+--------------------------------------------------+
The right answer is that the required IQ for part (b) is 73.6823.
To learn the subject better, go to web-site
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
and play there with free of charge online calculator.
Print the parameters in the calculator's window Area = 0.95, mean = 100, SD = 16
and specify the option "Above".
The calculator will give you the answer immediately and will show the area of interest.
Solved correctly for part (b).
After playing with this calculator 5 - 10 - 15 minutes, you will learn the subject
and will know it better than if 7 or 15 best teachers will explain to you during a semester.
If you have questions, come again to this forum soon ( ! )
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Specially for @CPhill:
(1) Your Artificial Intelligence will work perfectly,
if a 100% reliable person, like me, will accompany it,
fixing and repairing all possible future errors.
(2) If you want we, the tutors of this forum, be able to check
your posts/solutions, do not submit so many posts at once.
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